Well-posedness in the generalized sense for the incompressible Navier- Stokes equation (Q1186538)

The theory of well-posedness in the generalized sense is developed for the linearized, time-dependent Navier-Stokes equation for incompressible flow, together with boundary conditions. This concept of well-posedness means existence and uniqueness of solutions together with an energy estimate where the \(L_ 2\)-norm is taken not only over the space variables, but also over the time. We prove that the existence of a unique solution of the Laplace-Fourier transformed problem, together with the corresponding energy estimate, implies well-posedness in the generalized sense.